79 specifically specifically says that pursuing a judicial remedy under it is without prejudice to any available administrative or non-judicial remedy, including the right to lodge an Article 77 complaint. If this was meant as something that has to come after not getting satisfaction from an Article 77 complaint it would make no sense to say it is without prejudice to the right to lodge an article 77 complaint since that would have already had to have been lodged before getting here.
This also fits with what I saw on assorted EU and international law firm blogs, back when they were all writing articles on what GDPR would mean.
I did work on a GDPR compliance effort in an industry where it is big important (real time bidding ads) and our lawyers, while hedging, were not at all worried about random lawsuits. Their opinion was that we would easily be able to submit to the courts that the complaints needed to go through the authorities first.
If there are any, they probably won't be a big deal for the defendants. An individual lawsuit is limited to compensation for the damages suffered. In most cases, that just won't be very much, and so probably won't be worth the time and effort to pursue.
Only supervisory authorities can can impose punitive measures such as fines based on revenue. Those are the only things likely to actually make a difference.
Also I get the impression that European regulators are more responsive than US regulators. Europeans report things to regulators first and expect them to be taken care of. Contrast that to Americans who are far more likely to view the regulators as ineffective and turn first to a lawsuit.